TSTP Solution File: SYN014-2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN014-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n024.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 29 23:53:11 EDT 2022
% Result : Unsatisfiable 0.13s 0.36s
% Output : Proof 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 22
% Syntax : Number of formulae : 40 ( 10 unt; 4 typ; 0 def)
% Number of atoms : 145 ( 0 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 203 ( 96 ~; 92 |; 0 &)
% ( 15 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 2 ( 2 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 2 ( 1 >; 1 *; 0 +; 0 <<)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 86 ( 81 !; 0 ?; 86 :)
% Comments :
%------------------------------------------------------------------------------
tff(equalish_type,type,
equalish: ( $i * $i ) > $o ).
tff(n_type,type,
n: $i ).
tff(k_type,type,
k: $i ).
tff(m_type,type,
m: $i ).
tff(1,plain,
( equalish(n,k)
<=> equalish(n,k) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
equalish(n,k),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_20) ).
tff(3,plain,
equalish(n,k),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [Y: $i,X: $i] :
refl(
( ( ~ equalish(X,Y)
| equalish(Y,X) )
<=> ( ~ equalish(X,Y)
| equalish(Y,X) ) )),
inference(bind,[status(th)],]) ).
tff(5,plain,
( ! [Y: $i,X: $i] :
( ~ equalish(X,Y)
| equalish(Y,X) )
<=> ! [Y: $i,X: $i] :
( ~ equalish(X,Y)
| equalish(Y,X) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [Y: $i,X: $i] :
( ~ equalish(X,Y)
| equalish(Y,X) )
<=> ! [Y: $i,X: $i] :
( ~ equalish(X,Y)
| equalish(Y,X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(7,axiom,
! [Y: $i,X: $i] :
( ~ equalish(X,Y)
| equalish(Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetryish) ).
tff(8,plain,
! [Y: $i,X: $i] :
( ~ equalish(X,Y)
| equalish(Y,X) ),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
! [Y: $i,X: $i] :
( ~ equalish(X,Y)
| equalish(Y,X) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [Y: $i,X: $i] :
( ~ equalish(X,Y)
| equalish(Y,X) ),
inference(modus_ponens,[status(thm)],[9,5]) ).
tff(11,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ equalish(X,Y)
| equalish(Y,X) )
| ~ equalish(n,k)
| equalish(k,n) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ equalish(X,Y)
| equalish(Y,X) )
| ~ equalish(n,k)
| equalish(k,n) ) ),
inference(rewrite,[status(thm)],]) ).
tff(12,plain,
( ~ ! [Y: $i,X: $i] :
( ~ equalish(X,Y)
| equalish(Y,X) )
| ~ equalish(n,k)
| equalish(k,n) ),
inference(quant_inst,[status(thm)],]) ).
tff(13,plain,
( ~ ! [Y: $i,X: $i] :
( ~ equalish(X,Y)
| equalish(Y,X) )
| ~ equalish(n,k)
| equalish(k,n) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
equalish(k,n),
inference(unit_resolution,[status(thm)],[13,10,3]) ).
tff(15,plain,
( equalish(m,k)
<=> equalish(m,k) ),
inference(rewrite,[status(thm)],]) ).
tff(16,axiom,
equalish(m,k),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_23) ).
tff(17,plain,
equalish(m,k),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
( ~ equalish(m,n)
<=> ~ equalish(m,n) ),
inference(rewrite,[status(thm)],]) ).
tff(19,axiom,
~ equalish(m,n),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_19) ).
tff(20,plain,
~ equalish(m,n),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(X,Y)
| equalish(X,Z)
| ~ equalish(Y,Z) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(X,Y)
| equalish(X,Z)
| ~ equalish(Y,Z) ) ),
inference(rewrite,[status(thm)],]) ).
tff(22,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(X,Y)
| equalish(X,Z)
| ~ equalish(Y,Z) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(X,Y)
| equalish(X,Z)
| ~ equalish(Y,Z) ) ),
inference(rewrite,[status(thm)],]) ).
tff(23,plain,
^ [Z: $i,Y: $i,X: $i] :
rewrite(
( ( ~ equalish(X,Y)
| ~ equalish(Y,Z)
| equalish(X,Z) )
<=> ( ~ equalish(X,Y)
| equalish(X,Z)
| ~ equalish(Y,Z) ) )),
inference(bind,[status(th)],]) ).
tff(24,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(X,Y)
| ~ equalish(Y,Z)
| equalish(X,Z) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(X,Y)
| equalish(X,Z)
| ~ equalish(Y,Z) ) ),
inference(quant_intro,[status(thm)],[23]) ).
tff(25,axiom,
! [Z: $i,Y: $i,X: $i] :
( ~ equalish(X,Y)
| ~ equalish(Y,Z)
| equalish(X,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivityish) ).
tff(26,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ equalish(X,Y)
| equalish(X,Z)
| ~ equalish(Y,Z) ),
inference(modus_ponens,[status(thm)],[25,24]) ).
tff(27,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ equalish(X,Y)
| equalish(X,Z)
| ~ equalish(Y,Z) ),
inference(modus_ponens,[status(thm)],[26,22]) ).
tff(28,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ equalish(X,Y)
| equalish(X,Z)
| ~ equalish(Y,Z) ),
inference(skolemize,[status(sab)],[27]) ).
tff(29,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ equalish(X,Y)
| equalish(X,Z)
| ~ equalish(Y,Z) ),
inference(modus_ponens,[status(thm)],[28,21]) ).
tff(30,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(X,Y)
| equalish(X,Z)
| ~ equalish(Y,Z) )
| equalish(m,n)
| ~ equalish(m,k)
| ~ equalish(k,n) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(X,Y)
| equalish(X,Z)
| ~ equalish(Y,Z) )
| equalish(m,n)
| ~ equalish(m,k)
| ~ equalish(k,n) ) ),
inference(rewrite,[status(thm)],]) ).
tff(31,plain,
( ( ~ equalish(m,k)
| equalish(m,n)
| ~ equalish(k,n) )
<=> ( equalish(m,n)
| ~ equalish(m,k)
| ~ equalish(k,n) ) ),
inference(rewrite,[status(thm)],]) ).
tff(32,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(X,Y)
| equalish(X,Z)
| ~ equalish(Y,Z) )
| ~ equalish(m,k)
| equalish(m,n)
| ~ equalish(k,n) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(X,Y)
| equalish(X,Z)
| ~ equalish(Y,Z) )
| equalish(m,n)
| ~ equalish(m,k)
| ~ equalish(k,n) ) ),
inference(monotonicity,[status(thm)],[31]) ).
tff(33,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(X,Y)
| equalish(X,Z)
| ~ equalish(Y,Z) )
| ~ equalish(m,k)
| equalish(m,n)
| ~ equalish(k,n) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(X,Y)
| equalish(X,Z)
| ~ equalish(Y,Z) )
| equalish(m,n)
| ~ equalish(m,k)
| ~ equalish(k,n) ) ),
inference(transitivity,[status(thm)],[32,30]) ).
tff(34,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(X,Y)
| equalish(X,Z)
| ~ equalish(Y,Z) )
| ~ equalish(m,k)
| equalish(m,n)
| ~ equalish(k,n) ),
inference(quant_inst,[status(thm)],]) ).
tff(35,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(X,Y)
| equalish(X,Z)
| ~ equalish(Y,Z) )
| equalish(m,n)
| ~ equalish(m,k)
| ~ equalish(k,n) ),
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
$false,
inference(unit_resolution,[status(thm)],[35,29,20,17,14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SYN014-2 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n024.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Mon Sep 5 01:06:03 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.13/0.36 % SZS status Unsatisfiable
% 0.13/0.36 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------